We define a bow-tie quadrilateral as a quadrilateral where two sides cross each other. An example of a bow-tie quadrilateral is shown below. Seven distinct points are chosen on a circle. We draw all $\binom{7}{2} = 21$ chords that connect two of these points. Four of these $21$ chords are selected at random. What is the probability that these four chosen chords form a bow-tie quadrilateral?
Answers
Four chosen chords form a bow-tie quadrilateral 2210 .
What is a quadrilateral?A quadrilateral is a polygon having four sides, four angles, and four vertices. The word 'quadrilateral' is derived from the Latin words 'quadri,' which means four, and 'latus', which means side. The above image is an example of a quadrilateral.The bowtie, or crossed rectangle, is a nonconvex semi-uniform quadrilateral with the same vertices as a rectangle but with two of the original sides removed and with the original's diagonals in place instead.Given,
We are aware that a quadrilateral requires four vertices (or points on the circle). The cross can always be connected in one of two ways: horizontally or vertically. My understanding of combinations is inadequate, but we can deduce that picking four points from a possible seven equals 21. Four points can be used to create 21*2 = 42 "bow-tie quadrilaterals" on the circle by multiplying the two methods to join those lines (again, horizontally and vertically). Since there are 2210 possible combinations of four chords out of a possible 21 chords, the probability is 42/2210, and we just need to reduce that fraction.Therefore, Four chosen chords form a bow-tie quadrilateral 2210 .
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The probability that the four chosen chords form a bow-tie quadrilateral is: 60%.
First, let's calculate the total number of ways to choose four chords out of the 21 available chords.
= 21!/ 4! (21-4)!
= 21! / 4! 17!
= 5985
The number of ways to choose two intersecting chords can be represented as [tex]\binom{7}{2}.[/tex]
= 7! / (7-2)!
= 7!/ 5! 2!
= 7 x 6/ 2
= 21
However, we also need to account for the fact that we are choosing four chords in total.
So we need to choose two more chords from the remaining 19 chords.
C(19, 2)= 19!/{2!(19-2)!
= 19! / 2! 17!
= 19 x 18 /2
= 171
Now, the number of ways to choose four chords that form a bow-tie quadrilateral
= 21x 17
= 3591
Therefore, the probability that the four chosen chords form a bow-tie quadrilateral is:
= [tex]$\frac{\text{Number of ways to choose four chords forming a bow-tie quadrilateral}}{\text{Total number of ways to choose four chords}}[/tex]
= 3591/5985
= 0.600
So, the probability is 0.600, or 60%.
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Related Questions
Use the sample data and confidence level given below to complete parts (a) through (d).
A drug is used to help prevent blood clots in certain patients. In clinical trials, among 4144 patients treated with the drug, 124
developed the adverse reaction of nausea. Construct a 99% confidence interval fof the proportion of adverse reactions.
a) Find the best point estimate of the population proportion p.
(Round to three decimal places as needed.)
b) Identify the value of the margin of error E.
E-O
(Round to three decimal places as needed.)
c) Construct the confidence interval
(Round to three decimal places as needed)
d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below.
O A. One has 99% confidence that the interval from the lower bound to the upper bound actually does contain the true
value of the population proportion.
Answers
Answer:
Given that,
Sample size,
n
=
4369
Sample proportion,
^
p
=
185
4369
=
0.0423
a)
The sample proportion is a point estimate of the population proportion.
^
p
=
0.0423
b)
The margin of error is defined as:
M
E
=
Z
0.10
/
2
×
√
^
p
(
1
−
^
p
)
n
Excel function for the confidence coefficient:
=NORMINV(0.10/2,0,1)
M
E
=
1.645
×
√
0.0423
(
1
−
0.0423
)
4369
M
E
=
0.005
c)
The 90% confidence interval for the population proportion is defined as:
^
p
±
z
0.10
/
2
√
^
p
(
1
−
^
p
)
n
0.0423
±
1.645
√
0.0423
(
1
−
0.0423
)
4369
(
0.0373
,
0.0473
)
Rectangle has a perimeter of 48". The length is 4" more than the width. What is the length?
Answers
A rectangle has 4 sides. Two of the sides have the same length, and the other two sides have the same length. Therefore, two sides are x+4 and the other two are equal to x.
Your equation will be (x+4)+(x+4)+x+x=48
When you solve for x, you get 10.
Since your length is x+4, you will do 4+10 which is 14 as your final answer
FINAL ANSWER: 14''
Please let me know if this helped you!!
Answer:. Width=10 Length = 14
Step-by-step explanation:
2w + 2(w+4) = 48
2w +2w + 8 = 48
4w = 48-8
4w = 40
W=10. L= 14
10+10+14+14 = 48
Find the missing side lengths. Leave your answers as radicals in simplest form.
10 POINTS!!! ANSWER PLZ
Answers
Answer:
D.
[tex]u =3[/tex]
[tex]v =\sqrt{3}[/tex]
Step-by-step explanation:
Given
The triangle in the diagram above
Required
Find the missing lengths, u and v
To find the missing lengths, we have to check the relationship between the missing lengths, the given length and the given angle;
From trigonometry;
[tex]sin\ \theta = \frac{Opp}{Hyp}[/tex]; Where Opp = Opposite and Hyp = Hypotenuse
From the attached diagram;
[tex]\theta = 30[/tex]
[tex]Opp = v[/tex]
[tex]Hyp = 2\sqrt{3}[/tex]
[tex]sin\ \theta = \frac{Opp}{Hyp}[/tex] becomes
[tex]sin\ 30 = \frac{v}{2\sqrt{3}}[/tex]
Multiply both sides by [tex]2\sqrt{3}[/tex]
[tex]2\sqrt{3} * sin\ 30 = \frac{v}{2\sqrt{3}} * 2\sqrt{3}[/tex]
[tex]2\sqrt{3} * sin\ 30 = v[/tex]
In radians, [tex]sin30 = \frac{1}{2}[/tex]
[tex]2\sqrt{3} * \frac{1}{2} = v[/tex]
[tex]\sqrt{3} = v[/tex]
[tex]v =\sqrt{3}[/tex]
Similarly, From trigonometry;
[tex]cos\ \theta = \frac{Adj}{Hyp}[/tex]; Where Adj = Adjacent
From the attached diagram;
[tex]\theta = 30[/tex]
[tex]Adj = u[/tex]
[tex]Hyp = 2\sqrt{3}[/tex]
[tex]cos\ \theta = \frac{Adj}{Hyp}[/tex] becomes
[tex]cos\ 30 = \frac{u}{2\sqrt{3}}[/tex]
Multiply both sides by [tex]2\sqrt{3}[/tex]
[tex]2\sqrt{3} * cos\ 30 = \frac{u}{2\sqrt{3}} * 2\sqrt{3}[/tex]
[tex]2\sqrt{3} * cos\ 30 = u[/tex]
In radians, [tex]cos30 = \frac{\sqrt{3}}{2}[/tex]
[tex]2\sqrt{3} * \frac{\sqrt{3}}{2} = u[/tex]
[tex]\sqrt{3} * \sqrt{3} = u[/tex]
[tex]3 = u[/tex]
[tex]u =3[/tex]
If you have a gerbil, then you are a pet owner. Question 7 options: If you are not a gerbil, then you are not a pet owner. True If you are not a pet owner, then you have a gerbil. False; if you are not a pet owner then you have no pets. If you do not have a gerbil, then you are not a pet owner. False; you could have a dog. If you are not a pet owner, then you do not have a gerbil. True
Answers
Step-by-step explanation:
If you are not a gerbil, then you are not a pet owner. False; if you are not a gerbil, you can be a human who owns pets.
If you are not a pet owner, then you have a gerbil. False; if you are not a pet owner then you have no pets.
If you do not have a gerbil, then you are not a pet owner. False; you could have a dog or a cat.
If you are not a pet owner, then you do not have a gerbil. True, since if you do not own any pets, you will not have any animals, so you will not have a gerbil.
Hope this helps!
Answer:
If you are not a pet owner, then you have a gerbil. False; if you are not a pet owner then you have no pets
Step-by-step explanation:
helppp me plz im begging u
Answers
Answer:
The answer is 1
Step-by-step explanation:
You can try out all the numbers one by one but I'll just show you why 1 works.
First you need to replace x with 1:
-1+8>6
-1+8=7
7 is greater than 6 so 1 is the answer.
I hoped that helped!
(Brainliest???)
:)
Two parallel lines are 7 units apart. If you
reflect a shape over both, how far apart will the
preimage and final image be?
Answers
Answer:
14 units
Step-by-step explanation:
We apply the Theorem of reflection over parallel lines.
Theorem: The composition of two reflections over parallel lines that are h units apart is the same as a translation of 2h units.
Given that the two parallel lines are 7 units apart
h=7 units
2h= 2 X 7 =14 units
Therefore, the preimage and the final image will be 14 units apart.
There is a equilateral triangle with sides of 13 inches, how do I find the area of that triangle?
Answers
Answer:
73.18
Step-by-step explanation:
equilateral triangle means all sides are the same
A=(√3/4)a^2
A=(√3/4)*13^2
A=73.18 inches square
Answer:
73.18 square inches.
Step-by-step explanation:
To find the area of an equilateral triangle, we use a certain formula.
Where the side length is represented by s, the area is (sqrt(3))/4 * s^2.
Since s = 13, you will have (sqrt(3))/4 * 13^2 = 1.732050808/4 * 169 = 292.7165865/4 = 73.17914662. You can round that to 73.18.
So, the area of the triangle is 73.18 square inches.
Remember to use your units when presenting your answer, and hope this helps!
What is the volume of a right triangular pyramid whose base is 5 meters on each side and whose altitude is 4 meters?
Answers
Answer: 10 for each side but in total is 20
Step-by-step explanation: u multiply 5 x 4 = 20 divided by 2 to get 10 meters and another is 4 divided by 2 is 2 x 5 is 10 meters times 2 is 20 total
Find the zeros of y = x2 - 6x - 4 by completing the square.
A. x=-34/13
B. X- 3+ 118
CX13
D. x 316
Answers
Answer:
x = 3 ± [tex]\sqrt{13}[/tex]
Step-by-step explanation:
Given
y = x² - 6x - 4
To find the zeros let y = 0, that is
x² - 6x - 4 = 0 ( add 4 to both sides )
x² - 6x = 4
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 3)x + 9 = 4 + 9 , that is
(x - 3)² = 13 ( take the square root of both sides )
x - 3 = ± [tex]\sqrt{13}[/tex] ( add 3 to both sides )
x = 3 ± [tex]\sqrt{13}[/tex] ← exact solutions
4 Assuming the triangle was made of a material of uniform thickness which of the centres would also be the
centre of gravity of the triangle? Support your choice.
Answers
Step-by-step explanation:
you can split triangle in two 90-:80 triangles
Find the missing side length in the image attached.
Answers
Answer:
? = 35.
Step-by-step explanation:
According to the diagram...
? / 42 = 30 / (66 - 30)
? / 42 = 30 / 36
? / 42 = 5 / 6
6 * ? = 42 * 5
? = 7 * 5
? = 35
Hope this helps!
Answer: 35
Step-by-step explanation:
Set up the proportion as follows:
[tex]\dfrac{66}{30}=\dfrac{42+x}{x}\\\\\\66x=30(42+x)\\\\\\66x=1260+30x\\\\\\36x=1260\\\\\\x=\dfrac{1260}{36}\\\\\\x=\large\boxed{35}[/tex]
please help! enter a range of values for x:
Answers
Answer:
Step-by-step explanation:
x=27.8
In a group of 20 students, 7 study both Art and Biology. 5 study Biology but not Art. 8 study neither subject. Given that a randomly selected student studies Art, what is the probability the student studies Art and Biology?
Answers
Answer:
7:20
Step-by-step explanation:
Line m passes through the points (-4, 3) and (-4, 7). What is the slope of the line that is parallel to line m?
Answers
Answer:
4x
Step-by-step explanation:
When you have a parallel line, the slope of the line is the same. So the slope of (-4,3),(-4,7)=4 would be the same as for example 4x+5
What is the distance between the points (7 , 35) and (7 , 21) in the coordinate plane? A. 7 units B. 56 units C. 28 units D. 14 units
Answers
Answer:
14 unitsOption D is the correct option.
Step-by-step explanation:
Let the points be A and B
A ( 7 , 35 ) -----> ( x1 , y1 )
B ( 7 , 21 ) -------> ( x2 , y2 )
Now, finding the distance between these two points:
[tex] \sqrt{(x2 - x1) ^{2} + {(y2 - y1)}^{2} } [/tex]
Plug the values
[tex] = \sqrt{(7 - 7) ^{2} + {(21 - 35)}^{2} } [/tex]
[tex] = \sqrt{ {0}^{2} + {( - 14)}^{2} } [/tex]
0 raised to any positive power equals 0
[tex] = \sqrt{0 + {( - 14)}^{2} } [/tex]
When adding or subtracting 0, the quantity doesn't change
[tex] = \sqrt{ {( - 14)}^{2} } [/tex]
Reduce the index of the radical and exponent with 2
[tex] = 14 \: units[/tex]
Hope this helps...
Best regards!
~ a music lover
In △ABC, AB = BC = 20 and DE ≈ 9.28. Approximate BD.
Answers
Answer:
BD = 5
Step-by-step explanation:
∠A = 60°
Since AB = 20 = BC, Then ∠B = 60° resulting in a equilateral triangle with ∠C = 60°. Then dividing ∠DAE into half gives 4 = angles of 15° yielding each secition of BC being equal to 20/4 = 5. Do i don't think DE ≈ 9.28 cannot occur.
A tank can be filled by one pump in 50 minutes and by another in 60 minutes. A third pump can drain the tank in 75 minutes. If all 3 pumps work simultaneously, how long will it take to fill the tank? (Answer in hours)
Answers
let's label each pump A, B, and C, just for convenience. A fills the tank by 1/50 every minute, B fills the tank by 1/60 every minute, and C drains it by 1/75 every minute. Now we can put them all into one function: t(1/50 + 1/60 - 1/75) = 1, where t = our time in minutes and 1 = the tank being full.
next, we solve for t: t = 300/7 minutes, or approximately 42.86 minutes.
In chemistry laboratory, Maria put a liquid solution of sodium chloride in
two flasks. She put 0.25 mL of the solution in one flask and 1.75 mL of
the solution in the other flask.
Find the total amount of the liquid sodium chloride solution using
significant digits.
Answers
Answer:
[tex]Total = 2.00mL[/tex]
Step-by-step explanation:
Given
Solution: NaCl
Flask 1: 0.25mL of NaCl
Flask 2: 1.75mL of Nacl
Required
Calculate the total amount of the solution
The total amount of the solution is calculated by adding the size of the contents in both flasks
i,e,
[tex]Total = Flask\ 1 + Flask\ 2[/tex]
[tex]Total = 0.25mL + 1.75mL[/tex]
[tex]Total = 2.00mL[/tex]
Answer:
yep it is 2.00
Step-by-step explanation:
AD= 36 cm. Points C, B∈AD, such that AB:BC:CD=2:3:4. Find the distance of midpoints of the segments AB and CD. HELP ASAP PLZ will give brainiest if u get it right!
Answers
Answer:
Distance of midpoints of the segments AB and CD is 24 cm.
Step-by-step explanation:
Given that
AD = 36 cm
Points C and B are in segment AB.
The ratio of distance AB:BC:CD = 2:3:4
To find:
Distance of midpoints of the segments AB and CD ?
Solution:
The ratio of distance AB:BC:CD =2:3:4
Let AB = [tex]2x[/tex]
Let BC = [tex]3x[/tex]
Let CD = [tex]4x[/tex]
Now, it is clear that AD = AB + BC + CD
[tex]\Rightarrow 36=2x+3x+4x\\\Rightarrow 36=9x\\\Rightarrow x = 4\ cm[/tex]
Putting the value of x to find AB, BC and CD:
AB = [tex]2\times 4 = 8\ cm[/tex]
BC = [tex]3\times 4 = 12\ cm[/tex]
CD = [tex]4 \times 4 = 16\ cm[/tex]
Now, mid point of AB will be [tex]\frac{8}2 = 4\ cm[/tex] on the right side of point A.
And
mid point of CD will be [tex]\frac{16}2 = 8\ cm[/tex] on the left side of point D.
[tex]\therefore[/tex] If we subtract 4 and 8 from AD we will get distance between mid points of segments AB and CD.
So, Distance of midpoints of the segments AB and CD = 36 - 4 -8 = 24 cm.
Distance of midpoints of the segments AB and CD is 24 cm.
y is directionally proportional to x
When y = 21, x = 5
Write an equation for y in terms of x
Answers
Answer:
y = 21/5x
Step-by-step explanation:
y is directly proportional to x
y = kx
Find k constant.
21 = 5k
21/5 = k
Plug k as 21/5.
y = 21/5x
Answer:
y=21/5x
Step-by-step explanation:
When y is 21, x is 5.
5(21/5)=21, so we have y=21/5x
Which equation can be used to solve for the measure of angle ABC? tan(x) = tan(x) = sin(x) = sin(x) =
Answers
Answer:
A. tan(x) = 2.4/10
Step-by-step explanation:
The question is incomplete and lacks the required diagram. Find the question and diagram attached below.
Which equation can be used to solve for the measure of angle ABC? tan(x) = 2.4/10 tan(x) =10/2.4 sin(x) =10/10.3 sin(x) =10.3/10
We will use the SOH CAH TOA identity to calculate the equation needed to solve for angle ABC.
In a right angled triangle, the side facing the acute angle ABC is the opposite, the longest side is the hypotenuse and the third side (base) is the adjacent.
From the diagram shown;
AB = hypotenuse = 10.3cm
AC = opposite = 2.4cm
BC = adjacent = 10cm
To get the angle x, we can use the SOH and TOA identity.
SOH means sin<ABC = opp/hyp
Sin(x) = AC/AB = 2.4/10.3
TOA ≈ Tan(x) = opp/adj
Tan(x) = 2.4/10
The equation that can be used to solve for the measure of angle ABC are therefore sin(x) = 2.4/10.3 OR tan(x) = 2.4/10
Based on the given option,
tan(x) = 2.4/10 is the only correct answer.
Answer:
in short its A.
Step-by-step explanation:
EDGE 2021
How many 4-digit numbers can be formed using only the digits 9, 8 and 7?
Answers
Answer:
isnt it 0
Step-by-step explanation:
They only gave 3 digits
2/3x + 2= 21/3 solve for x a. 0 b. 1/2 c -2 d. 2
Answers
Answer:
x = 7.5
Step-by-step explanation:
2/3x + 2= 21/3
Subtract 2 from each side
2/3x + 2-2= 21/3-2
2/3x = 21/3 - 6/3
2/3x =15/3
2/3x = 5
Multiply each side by 3/2 to isolate x
2/3x * 3/2 = 5 *3/2
x = 15/2
Write an explicit formula for An, the nth term of the sequence 1, -2, 4, ....
Answers
Answer:
an = (-2)^(n - 1)
Step-by-step explanation:
a1 = 1
a2 = 1 * (-2) = -2
a3 = a2 * (-2) = (-2) * (-2) = (-2)^2
a4 = a3 * (-2) = (-2)^3
etc.
an = (-2)^(n - 1)
Answer:
(-2)^n-1
Step-by-step explanation:
got it right on delta
Which of the following inequalities could be represented by the graph?
Answers
PLEASE HELP ME!!! I NEED THIS REALLY SOON OR I WILL FAIL! What are some measurements that might be easier if we worked in the metric system like the rest of the world? Explain your answer.
Answers
Answer:
Centimeters might be easier because they can be much more precise than inches when there isn't an ideal length. Kilometers might be easier because it would not require such large numbers to work with.
Step-by-step explanation:
:)
Tom has 4 navy socks and 6 black socks in a drawer. One dark morning he randomly pulls if 2 socks. What is the probability that he will selects a pair of navy socks ?
Answers
Answer:
1/5
Step-by-step explanation:
total number of socks= 10
randomly selects two socks.
2/10=1/5 probability
1. A population of 20 rabbits is released into a wildlife region. The population is growing at a rate of 60% per year. What is the population of rabbits after 8 years and what equation did you use? 2. The population of white rhinos in 2001 was 11,670. The population is declining by 9% each year. What is the population expected to be in the year 2021 and what equation did you use?
Answers
Answer:
I think it's 12
Step-by-step explanation:
i just multiplied 60 by 20%
Ok I added the Pics to make it easy
Answers
Answer:
Bill and Ted are going to order t-shirts for there school clubs. The t-shirts will have the club logo printed on the front. Bill and Ted ask two local t-shirt companies to give them a price. * Patty's Printing charges $21.50 for each t-shirt. * Sandra's shirts has a one-time set up fee for $63 and then charges $18 for each t-sh
Step-by-step explanation:
Part 2: Table Chart:
Number of t-shirts: 2
Patty's cost: 43$
Sandra's cost: : 99$
Number of t-shirts: 4
Patty's cost: 86$
Sandra's cost: : 135$
Number of t-shirts: 6
Patty's cost: 129$
Sandra's cost: : 171$
Number of t-shirts: 8
Patty's cost: 172$
Sandra's cost: : 207$
Number of t-shirts: 10
Patty's cost: 215$
Sandra's cost: : 243$
Number of t-shirts: 12
Patty's cost: 258$
Sandra's cost: : 279$
Number of t-shirts: 14
Patty's cost: 301$
Sandra's cost: : 315$
Number of t-shirts: 16
Patty's cost: 344$
Sandra's cost: : 351$
Number of t-shirts: 18
Patty's cost: 387$
Sandra's cost: : 387$
Part 3: Patty's Printing
Linear equation = equation of a line= y=mx+b
y=21.5x
Part 4: Sandra's Shirts:
Linear equation = equation of a line= y=mx+b
y= 18x+63
Part 5: Note to Jackie
Dear Jackie, I recommend Sandra's shirts.
Write equations:
Sandra's Shirts = 18x+63
Patty's Printing = 21.5x
Sandra's Shirts: 495=18x+63 = 24 shirts
Patty's Printing: 495=21.5x = 23 shirts
Part 6: Refute Jackie
Sandra's Shirts is more expensive at the beginning, but as you buy more shirts (greater than 18), Patty's Printing becomes cheaper.
You should probably add to this, but I can't think of anything else.
Part 7: Equality
At 18 shirts (see table), the shirt cost is equal.
You should probably add to this, but I can't think of anything else.
18x+63=21.5x
Words of encouragement:
Good luck!
If the tangent value is 33*, the cotangent value to the hundredths degree is: 0.65 0.649 1.54 1.540
Answers
Answer:
1.54
Step-by-step explanation:
The cotangent value is referred to as the reciprocal or the opposite of a given tangent value. Cotangent is also referred to as it's short form called cot
Mathematically, Cotangent (cot) = 1/tan
In the above question, we are given a value where:
tan = 33°
Cotangent (cot) = 1/tan 33°
Cotangent (cot) = 1.5398649638
We are told to approximate to the nearest hundredth
= 1.54